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Singular curves are treated through a detailed study of the Picard group.  The second part starts with blowing-ups and desingularisation (embedded or not) of fibered surfaces over a Dedekind ring that leads on to intersection theory on arithmetic surfaces. Castelnuovo's criterion is proved and also the existence of the minimal regular model. This leads to the study of reduction of algebraic curves. The case of elliptic curves is studied in detail. The book concludes with the fundamental theorem of stable reduction of Deligne-Mumford.  This book is essentially self-contained, including the necessary material on commutative algebra. The prerequisites are few, and including many examples and approximately 600 exercises, the book is ideal for graduate students.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ GARDNERS","offer_id":49727623201041,"sku":"NGR9780199202492","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ NEW \/ INGRAM","offer_id":51223088169233,"sku":"NIN9780199202492","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52429794279697,"sku":"NLS9780199202492","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0199202494.jpg?v=1751005603"},{"product_id":"metallurgical-process-simulation-and-optimization-book-qing-liu-9783036564302","title":"Metallurgical Process Simulation and Optimization","description":null,"brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52669895442705,"sku":"NLS9783036564302","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":53367563747601,"sku":"NIN9783036564302","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783036564302.jpg?v=1762288492"},{"product_id":"data-provenance-and-data-management-in-escience-book-qing-liu-9783642441585","title":"Data Provenance and Data Management in eScience","description":"eScience allows scientific research to be carried out in highly distributed environments. 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